Triangles k l p and q m n are shown. triangle q m n is slightly higher than triangle k l p and side q m connects to side k p. point m is at the midpoint of k p. sides k l and q n are congruent. angles k l p and q n m are congruent. angles k p l and q m n are both right angles. is there a series of rigid transformations that could map triangleklp to triangleqnm? if so, which transformations? no, triangleklp and triangleqnm are congruent but triangleklp cannot be mapped to triangleqnm using a series rigid transformations. no, triangleklp and triangleqnm are not congruent. yes, triangleklp can be reflected across the line containing kp and then translated so that p is mapped to m. yes, triangleklp can be rotated about p and then translated so that l is mapped to n.

Arecent study focused on the number of times men and women who live alone buy take-out dinner in a month. assume that the distributions follow the normal probability distribution and the population standard deviations are equal. the information is summarized below. statistic men women sample mean 24.85 21.33 sample standard deviation 5.54 4.93 sample size 34 36 at the 0.01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month? state the decision rule for 0.01 significance level: h0: μmen= μwomen h1: μmen ≠ μwomen. (negative amounts should be indicated by a minus sign. round your answers to 3 decimal places.) compute the value of the test statistic. (round your answer to 3 decimal places.) what is your decision regarding the null hypothesis? what is the p-value? (round your answer to 3 decimal places.)